For cake: Preheat oven to 325°F Butter two 9-inch-diameter cake pans with 2-inch-high sides; line bottoms with parchment paper rounds. Dust pans with flour; tap out excess. Melt chocolate in top of double boiler over simmering water, stirring until melted and smooth. Remove from over water. Cool to lukewarm. Whisk flour, baking soda, and salt in medium bowl. Using electric mixer, beat sugar, butter, and vanilla in large bowl to blend. Add eggs 1 at a time, beating well after each addition and stopping occasionally to scrape down sides of bowl. Gradually beat in lukewarm melted chocolate. Beat in dry ingredients in 3 additions alternately with sour cream in 2 additions, beginning and ending with dry ingredients. Gradually beat in crème de cacao and coffee. Divide batter evenly between prepared pans; smooth tops.
Bake cakes until toothpick inserted into centers comes out clean, about 35 minutes. Cool cakes in pans on racks 10 minutes. Invert cakes onto 9-inch cardboard rounds or removable tart pan bottoms; cool cakes completely on racks.
For buttercream: Melt milk chocolate in top of double boiler over simmering water, stirring until smooth. Remove from over water. Whisk sugar, egg yolks, 2 tablespoons water, and corn syrup in medium metal bowl to blend. Add 1/4 cup butter. Set bowl over saucepan of simmering water; whisk constantly until mixture reaches 170°F, about 4 minutes. Remove bowl from over water. Using electric mixer, beat until completely cool and thick, about 6 minutes. Gradually beat in 1/2 cup butter, about 1 tablespoon at a time, fully incorporating each addition and stopping occasionally to scrape down sides of bowl. Beat in lukewarm melted chocolate.
For coffee mousse:Bring half and half, 2 tablespoons sugar, and espresso powder to simmer in small saucepan over medium-high heat. Whisk egg yolks and remaining 2 tablespoons sugar in medium bowl to blend. Gradually whisk hot half and half mixture into yolk mixture. Return mixture to saucepan and stir constantly over medium heat until thermometer registers 160°F, about 2 minutes. Pour into large bowl. Add softened gelatin; stir until dissolved. Using electric mixer, beat until cool, about 10 minutes. Using clean dry beaters, beat cream and vanilla in medium bowl until stiff peaks form. Fold whipped cream into coffee mixture.
Cut each cake layer horizontally in half. Place 1 cake layer in bottom of 9-inch-diameter springform pan. Cover with 3/4 cup buttercream. Place second cake layer atop buttercream; cover with mousse. Top with third cake layer. Refrigerate 1 hour to allow mousse to set. Spread 3/4 cup buttercream over third cake layer. Top with fourth cake layer (cake will rise above rim of pan). Cover and refrigerate at least 4 hours or overnight.
For chocolate glaze: Stir sugar and 1 cup water in medium saucepan over medium heat until sugar dissolves. Increase heat to high; bring to boil. Whisk in cocoa; remove from heat. Add chocolate; whisk until smooth. Let stand until cool but still pourable, about 2 hours.
Run knife around pan sides to loosen cake. Release pan sides. Scrape excess mousse from sides of cake. Transfer cake on springform pan bottom to rack set over baking sheet. Pour glaze over cake, allowing glaze to drip down edges onto baking sheet (use spatula to spread glaze over any uncovered spots). Refrigerate at least 2 hours to allow glaze to set. (Can be made 1 day ahead. Keep refrigerated. Let stand at room temperature 1 hour before serving.).